In this paper, we shall investigate the symmetry property of a multivariate orthogonal M -refinable function with a general dilation matrix M . For an orthogonal M -refinable function φ such that φ is symmetric about a point (centro-symmetric) and φ provides approximation order k, we show that φ must be an orthogonal M -refinable function that generates a generalized coiflet of order k. Next, w...

Let Φ be an irreducible crystallographic root system with Weyl group W and coroot lattice Q̌, spanning a Euclidean space V . Let m be a positive integer and AmΦ be the arrangement of hyperplanes in V of the form (α, x) = k for α ∈ Φ and k = 0, 1, . . . ,m. It is known that the number N(Φ, m) of bounded dominant regions of AmΦ is equal to the number of facets of the positive part ∆ m + (Φ) of the...

We study biharmonic hypersurfaces in a generic Riemannian manifold. We first derive an invariant equation for such hypersurfaces generalizing the biharmonic hypersurface equation in space forms studied in [16], [8], [6], [7]. We then apply the equation to show that the generalized Chen’s conjecture is true for totally umbilical biharmonic hypersurfaces in an Einstein space, and construct a (2-p...

We study here the elementary properties of the relative entropyH(A,B) = Tr[φ(A)−φ(B)−φ(B)(A−B)] for φ a convex function and A,B bounded self-adjoint operators. In particular, we prove that this relative entropy is monotone if and only if φ is operator monotone. We use this to appropriately define H(A,B) in infinite dimension. In this paper we introduce a relative entropy H(A,B) of two bounded o...

This paper characterizes the boundedness and compactness of the generalized composition operator (C φf)(z) = ∫ z 0 f ′(φ(ξ))g(ξ)dξ from Bloch type spaces to QK type spaces.

The purpose of this paper is to develop a fairly large number of sets of global parametric sufficient optimality conditions under various generalized (F, b, φ, ρ, θ)univexity assumptions for a continuous minmax fractional programming problem involving arbitrary norms.